In this topic you will explore the following concepts identifying quadratic equations, quadratic trinomials, quadratic binomials, solving quadratic equations using the Null Factor Law, factorising quadratics, completing the square (extension)
Abbreviations eso – every second one CAS – graphics calculator
Classroom Activities
Consolidation Tasks
Enrichment & Extension Activities
Homework
1
Learning Outcome – What is a Quadratic Equation? Students will identify which equations are ‘quadratic’ and which are not. In doing so, they will show their understanding of what a quadratic equation is.
Learning Outcome - Solving Quadratic Equations Students will use the Null Factor Law to solve quadratic equations
Worked Examples Pg 411 Ex 10B Q1abdegin Q4a
Pg 408 Ex 10A Q1 Puzzle 112
There is a PowerPoint for simple ‘taking out a common factor’ and it can be accessed at http://drp.bo/?MGSCYr9Maths
Maths Online à Quadratic Equations à Factored Equations à worksheet
Puzzle 115
Pg 411 Ex 10B Q5, Q6, Q7
30 minutes to Finish exercises, Puzzle 112 Puzzle 114, and review work
2
Learning Outcome - Factorising and Expanding Patterns Students will recognise two specific patterns of algebraic expressions and use this knowledge to assist in factorising expressions. The two patterns are: - The ‘difference of two squares’ rule
- The ‘perfect square’ rule
Notes & Worked Examples Pg 414 Ex 10C Q1, Q2, Q3, Q4, Q5, Q6
Pg 418 Ex 10D Q1abcdefgh, Q2abcdkl, Q4
Maths Online à Algebra à Factorisation à Difference of Two Squaresà worksheet
30 minutes to catch up on exercises, worksheets and review work
4
Learning Outcome - Factorising Quadratic trinomials Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form.
30 minutes to catch up on exercises and review work
5
Learning Outcome - Factorising Quadratic trinomials continued Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form.
30 minutes to catch up on exercises and review work
6
Learning Outcome - Factorising Quadratic trinomials Students will apply the process of ‘grouping 2 and 2’ so that they can express quadratic trinomials in factor form [Alternative method may also be explored]
30 minutes to catch up on exercises and review work
7
Learning Outcome - Solving Quadratic equations with 3 terms Students will apply what they have learnt in the last 6 lessons to solve quadratic equations.
Learning Outcome - Applications using Quadratic equations Students will convert sentences into math terms and then apply what they have learnt in this topic to solve worded problems.
Notes & Worked examples Pg 431-432 Ex 10I Q1, Q4, Q6, Q7, Q8, Q9, Q11
Extension Question for lesson 9
Economics tells us that the cheaper an item the more items we will sell.
Maddi is on a committee that is trying to raise money for World Challenge 2011 by selling traditional Moroccan craft items. Maddi needs to raise at least $800 for the Challenge. At $20 each, 30 craft items will be sold. For every $1 reduction in the price of the items, 5 more will be sold. In what price range should they be sold?
Let the discount in the price of the craft items be x. The price of the items will be given by (20 − x). The number of items sold will be 30 + 5x. The income from sales will be given by the price × the number sold. Write an expression for the income.
Maddi needs to raise at least $800 for the Challenge. Therefore, the income must equal $800. Form a quadratic equation by expanding (20 − x)(30 + 5x) = 800 and rewriting the equation in standard form.
Factorise and solve the quadratic equation to find two prices between which the Moroccan craft items should be priced.
Examine the equation in more detail to find the price at which the income will be greatest, and find what this maximum income is equal to.
identifying quadratic equations, quadratic trinomials, quadratic binomials, solving quadratic equations using the Null Factor Law, factorising quadratics, completing the square (extension)
eso – every second one CAS – graphics calculator
Students will identify which equations are ‘quadratic’ and which are not. In doing so, they will show their understanding of what a quadratic equation is.
Learning Outcome - Solving Quadratic Equations
Students will use the Null Factor Law to solve quadratic equations
Pg 411
Ex 10B Q1abdegin Q4a
Puzzle 112
There is a PowerPoint for simple ‘taking out a common factor’ and it can be accessed at http://drp.bo/?MGSCYr9Maths
Maths Online à Quadratic Equations à Factored Equations à worksheet
Puzzle 115
Puzzle 112
Puzzle 114, and review work
Students will recognise two specific patterns of algebraic expressions and use this knowledge to assist in factorising expressions. The two patterns are:
- The ‘difference of two squares’ rule
- The ‘perfect square’ rule
Pg 414 Ex 10C Q1, Q2, Q3, Q4, Q5, Q6
Pg 418 Ex 10D Q1abcdefgh, Q2abcdkl, Q4
Please view PowerPoint. Access it at
http://drp.bo/?MGSCYr9Maths
Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form.
‘Sums & products with directed numbers’
‘Introducing Factorising Quad Trinomials’
Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form.
Factorising QTs for monic quadrtics (a=1) Sheet 1 & Sheet 2
Puzzle 114
Students will apply the process of ‘grouping 2 and 2’ so that they can express quadratic trinomials in factor form
[Alternative method may also be explored]
Sheet 3 & Sheet 4
Q1 Choose 3 questions
Q2 Choose 3 questions
Students will apply what they have learnt in the last 6 lessons to solve quadratic equations.
‘Completing the Square’ worksheet
(30 minutes)
Students will convert sentences into math terms and then apply what they have learnt in this topic to solve worded problems.
Pg 431-432 Ex 10I Q1, Q4, Q6, Q7, Q8, Q9, Q11
Pg 438 Ex 10J
Extension Question for lesson 9
Economics tells us that the cheaper an item the more items we will sell.
Maddi is on a committee that is trying to raise money for World Challenge 2011 by selling traditional Moroccan craft items. Maddi needs to raise at least $800 for the Challenge. At $20 each, 30 craft items will be sold. For every $1 reduction in the price of the items, 5 more will be sold. In what price range should they be sold?